At move 10: White has more space (central space at that!), and black's bishop on c8 doesn't have much of a future with the b pawn blocked and white controlling the e5 square
At move 13: One of the main positional features is the open files, and white has better access as black's c8 bishop is interrupting heavy piece harmony on the 8th rank
However, your opponent trades one of their best pieces rather than activating the rooks or otherwise looking to improve. One way of figuring out whether to trade is to count the squares each piece contacts. In the position after a3 Bd7, white's dark square bishop contacts 7 squares while black's is in contact with 4......so why trade it!?
As for your play with black, it's a little unambitious out of the opening. 4...Nbd7 is off: It blocks the bishop on c8, defends a knight which isn't attacked, and has no square to go to except b6 which isn't exactly taking over the game. Stockfish gives dxc4, c5, and Bb4 - all of which are hitting the center.
After c6, you're transposing into a semi slav....but one with white's bishop on f4 which is quite nice for white. Usually, white is either stuck behind the e3 pawn or forced to enter complications with Bg5, so it's not necessarily a coup for white, but it's pleasant.
However, my engine is giving it as basically equal on move 10. Perhaps my potato laptop and outdated stockfish are being fooled by some incredible positional nuance, but black isn't losing. You're just accepting a slightly worse (but solid) position
According to chess.com's engine white is up a full point between moves 10 to 14 before it becomes equal again. I think I may have some problems playing against d4 queen's gambit type games as black for some reason I'll try find some old losses.